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Productively Lindelöf Spaces May All Be $D$
  Published:2011-08-03
 Printed: Mar 2013
Canadian Mathematical Bulletin
  • Franklin D. Tall,
    Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4
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Abstract

We give easy proofs that (a) the Continuum Hypothesis implies that if the product of $X$ with every Lindelöf space is Lindelöf, then $X$ is a $D$-space, and (b) Borel's Conjecture implies every Rothberger space is Hurewicz.
Keywords: productively Lindelöf, $D$-space, projectively $\sigma$-compact, Menger, Hurewicz productively Lindelöf, $D$-space, projectively $\sigma$-compact, Menger, Hurewicz
MSC Classifications: 54D20, 54B10, 54D55, 54A20, 03F50 show english descriptions Noncompact covering properties (paracompact, Lindelof, etc.)
Product spaces
Sequential spaces
Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
Metamathematics of constructive systems 54D20 - Noncompact covering properties (paracompact, Lindelof, etc.)
54B10 - Product spaces
54D55 - Sequential spaces
54A20 - Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
03F50 - Metamathematics of constructive systems
 
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